Nuclei are self-bound systems of interacting nucleons, whose unified description is made intricate by the very diverse phenomenology emerging in nuclear systems. Besides individual excitations responsible for absolute binding energies and separation energies between nuclei, long-range correlations with a high degree of collectivity play a major role in macroscopic properties of nuclei and are essential for comparison with experimental measurements.
In this thesis, the focus is put on microscopic models where the nucleus is described as a collection of point-like nucleons in strong interactions, falling into the realm of the quantum many-body problem. Two approaches exist to solve this problem, differing by the very nature of the interaction. Energy Density Functional (EDF) uses a phenomenological system-dependent Hamiltonian easily encompassing short-range correlations at the mean-field level, leaving long-range physics to be captured beyond the mean-field via multi-reference methods. On the contrary, ab initio methods start from a realistic interaction rooted (through chiral Effective Field Theory) into the underlying theory of the strong force, i.e. quantum chromo-dynamics, making the solution of the many-body problem much more difficult to compute but providing results that are more reliable and systematically improvable.
In the present work, a new multi-reference perturbation theory to solve the many-body problem starting from chiral interactions is formalized in order to include coherently long and short range correlations in both closed- and open-shell nuclei. The first order of this theory, directly adapted from the EDF know-how to the ab initio context, is benchmarked in large scale calculations against other methods, and applied to the Neon chain. The second - newly formalized - order of the theory is implemented in small-scale model spaces to assess the quality of the method and compared with available single-reference perturbative expansions. The novel formalism shows great promises to describe ground and excited states of closed and open-shell nuclei.